compilePointConstraints

Compile point constraints into equality and inequality systems.

Developer documentation: this item describes internal implementation details.

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Declaration

 [Aeq,beq,Aineq,bineq] = compilePointConstraints(pointConstraints,tKnot,K)

Parameters

• pointConstraints PointConstraint array
• tKnot per-dimension knot vectors
• K spline order per dimension

Returns

• Aeq equality-constraint matrix
• beq equality-constraint right-hand side
• Aineq inequality-constraint matrix
• bineq inequality-constraint right-hand side

Discussion

For each point constraint, this function evaluates the tensor-product basis or derivative row at the constrained points and turns the requested relation into linear constraints on the coefficient vector xi.

If a row of the evaluated basis is denoted by \(b_m^T\), then the three supported relations are compiled as

\[b_m^{T}\xi = v_m, \qquad b_m^{T}\xi \le v_m, \qquad b_m^{T}\xi \ge v_m,\]

with lower bounds rewritten as \(-b_m^T \xi \le -v_m\).

Rows sharing the same derivative order are batched together so the basis matrix only has to be evaluated once per derivative multi-index.